Integrais

tgx^4*secx = (sec²x-1)²secx = sec^5 - 2sec^3 + sec _______________________________________________________________________________ ? (sec(x))^n.dx = [sec(x)^(n-2)tg(x)]/(n-1) + (n-2)/(n-1)? (sec(x))^(n-2)dx _______________________________________________________________________________ ? tgx^4*secx.dx = ? sec^5.dx - ? 2sec^3.dx + ? sec.dx ? sec^5.dx = (tg.sec^3)/4 + 3/4? sec^3.dx ? tgx^4*secx.dx = (tg.sec^3)/4 -5/4? sec^3.dx + ? sec.dx ? sec^3.dx = (tg.sec)/2 + 1/2? sec.dx ? tgx^4*secx.dx = (tg.sec^3)/4 - 5/8(tg.sec) + 3/8? sec.dx ? sec.dx = ln|sec + tg| ? tgx^4*secx.dx = (tg.sec^3)/4 - 5/8(tg.sec) + 3/8ln|sec + tg| + C (Preciso conferir) ? tgh(x) sech^4(x)dx = ? senh(x)*cosh^(-5)(x)dx ___________________________________________________________ cosh(x)' = -senh(x) ___________________________________________________________ ? tgh(x) sech^4(x)dx = -(1/4)cosh^(-4) + C